1961 IMO Problems

Revision as of 10:29, 12 October 2007 by 1=2 (talk | contribs) (Problem 1)

Day I

Problem 1

(Hungary) Solve the system of equations:

$\begin{matrix} \quad x + y + z \!\!\! &= a \; \, \\ x^2 +y^2+z^2 \!\!\! &=b^2 \\ \qquad \qquad xy \!\!\!  &= z^2 \end{matrix}$

where $a$ and $b$ are constants. Give the conditions that $a$ and $b$ must satisfy so that $x, y, z$ (the solutions of the system) are distinct positive numbers.

Solution

Problem 2

Solution


Problem 3

Solution


Day 2

Problem 4

Solution


Problem 5

Solution


Problem 6

Solution



See Also

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